Using SPM 12’s Second-Level Bayesian Inference Procedure for fMRI Analysis: Practical Guidelines for End Users

Recent debates about the conventional traditional threshold used in the fields of neuroscience and psychology, namely P < 0.05, have spurred researchers to consider alternative ways to analyze fMRI data. A group of methodologists and statisticians have considered Bayesian inference as a candidate methodology. However, few previous studies have attempted to provide end users of fMRI analysis tools, such as SPM 12, with practical guidelines about how to conduct Bayesian inference. In the present study, we aim to demonstrate how to utilize Bayesian inference, Bayesian second-level inference in particular, implemented in SPM 12 by analyzing fMRI data available to public via NeuroVault. In addition, to help end users understand how Bayesian inference actually works in SPM 12, we examine outcomes from Bayesian second-level inference implemented in SPM 12 by comparing them with those from classical second-level inference. Finally, we provide practical guidelines about how to set the parameters for Bayesian inference and how to interpret the results, such as Bayes factors, from the inference. We also discuss the practical and philosophical benefits of Bayesian inference and directions for future research.

[1]  Hal S Stern,et al.  A Test by Any Other Name: P Values, Bayes Factors, and Statistical Inference , 2016, Multivariate behavioral research.

[2]  Jingyuan E. Chen,et al.  Influence of the cortical midline structures on moral emotion and motivation in moral decision-making , 2016, Behavioural Brain Research.

[3]  Roger D. Peng,et al.  The reproducibility crisis in science: A statistical counterattack , 2015 .

[4]  G. Gigerenzer Mindless statistics , 2004 .

[5]  Brian A. Nosek,et al.  Power failure: why small sample size undermines the reliability of neuroscience , 2013, Nature Reviews Neuroscience.

[6]  Thomas E. Nichols,et al.  Scanning the horizon: towards transparent and reproducible neuroimaging research , 2016, Nature Reviews Neuroscience.

[7]  Jeffrey N. Rouder,et al.  Bayesian t tests for accepting and rejecting the null hypothesis , 2009, Psychonomic bulletin & review.

[8]  R. Turner,et al.  Detecting Latency Differences in Event-Related BOLD Responses: Application to Words versus Nonwords and Initial versus Repeated Face Presentations , 2002, NeuroImage.

[9]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[10]  Stephen M. Smith,et al.  Threshold-free cluster enhancement: Addressing problems of smoothing, threshold dependence and localisation in cluster inference , 2009, NeuroImage.

[11]  W. Penny,et al.  Objective Bayesian fMRI analysis—a pilot study in different clinical environments , 2015, Frontiers in Neuroscience.

[12]  Leif D. Nelson,et al.  False-Positive Psychology , 2011, Psychological science.

[13]  William A. Cunningham,et al.  Type I and Type II error concerns in fMRI research: re-balancing the scale. , 2009, Social cognitive and affective neuroscience.

[14]  Jacob Cohen,et al.  A power primer. , 1992, Psychological bulletin.

[15]  Gabriele Lohmann,et al.  Bayesian second-level analysis of functional magnetic resonance images , 2003, NeuroImage.

[16]  Evan M. Gordon,et al.  Precision Functional Mapping of Individual Human Brains , 2017, Neuron.

[17]  William A. Cunningham,et al.  Tools of the Trade Type I and Type II error concerns in fMRI research : rebalancing the scale , 2009 .

[18]  A. Kilcoyne,et al.  Type I and Type II error , 2013 .

[19]  Karl J. Friston,et al.  Bayesian Treatments of Neuroimaging Data , 2006 .

[20]  Hyemin Han Neural correlates of moral sensitivity and moral judgment associated with brain circuitries of selfhood: A meta-analysis , 2017 .

[21]  P. Molenberghs,et al.  Common and distinct neural networks involved in fMRI studies investigating morality: an ALE meta-analysis , 2018, Social neuroscience.

[22]  S. Maxwell The persistence of underpowered studies in psychological research: causes, consequences, and remedies. , 2004, Psychological methods.

[23]  G H Glover,et al.  Image‐based method for retrospective correction of physiological motion effects in fMRI: RETROICOR , 2000, Magnetic resonance in medicine.

[24]  Thomas E. Nichols Multiple testing corrections, nonparametric methods, and random field theory , 2012, NeuroImage.

[25]  R. Lanfear,et al.  The Extent and Consequences of P-Hacking in Science , 2015, PLoS biology.

[26]  Hans Knutsson,et al.  Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates , 2016, Proceedings of the National Academy of Sciences.

[27]  Stanislas Dehaene,et al.  Origins of the brain networks for advanced mathematics in expert mathematicians , 2016, Proceedings of the National Academy of Sciences.

[28]  Guillaume Flandin,et al.  Bayesian Analysis of fMRI data with Spatial Priors , 2005 .

[29]  A. Glenn,et al.  Evaluating Methods of Correcting for Multiple Comparisons Implemented in SPM12 in Social Neuroscience fMRI Studies: An Example from Moral Psychology , 2017, bioRxiv.

[30]  H. Pashler,et al.  Editors’ Introduction to the Special Section on Replicability in Psychological Science , 2012, Perspectives on psychological science : a journal of the Association for Psychological Science.

[31]  N. Lazar,et al.  The ASA Statement on p-Values: Context, Process, and Purpose , 2016 .

[32]  Thomas E. Nichols,et al.  Controlling the familywise error rate in functional neuroimaging: a comparative review , 2003, Statistical methods in medical research.

[33]  Paul A. Taylor,et al.  FMRI Clustering in AFNI: False-Positive Rates Redux , 2017, Brain Connect..

[34]  Aaron M. Ellison,et al.  AN INTRODUCTION TO BAYESIAN INFERENCE FOR ECOLOGICAL RESEARCH AND ENVIRONMENTAL , 1996 .

[35]  James G. Scott,et al.  Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem , 2010, 1011.2333.

[36]  Hyemin Han,et al.  Evaluating Methods of Correcting for Multiple Comparisons Implemented in SPM12 in Social Neuroscience fMRI Studies: An Example from Moral Psychology , 2017, bioRxiv.

[37]  Thomas E. Nichols,et al.  Nonparametric permutation tests for functional neuroimaging: A primer with examples , 2002, Human brain mapping.

[38]  David Bolin,et al.  Fast Bayesian whole-brain fMRI analysis with spatial 3D priors , 2016, NeuroImage.

[39]  J. Ioannidis Why Most Published Research Findings Are False , 2005, PLoS medicine.

[40]  T. Naidich,et al.  Editorial , 1996, Neuroradiology.

[41]  G. Glover,et al.  Spiral‐in/out BOLD fMRI for increased SNR and reduced susceptibility artifacts , 2001, Magnetic resonance in medicine.

[42]  Jonathan D. Cohen,et al.  An fMRI Investigation of Emotional Engagement in Moral Judgment , 2001, Science.

[43]  Mark W. Woolrich,et al.  Bayesian inference in FMRI , 2012, NeuroImage.

[44]  Regina Nuzzo,et al.  Scientific method: Statistical errors , 2014, Nature.

[45]  Karl J. Friston,et al.  Posterior probability maps and SPMs , 2003, NeuroImage.

[46]  Catie Chang,et al.  Relationship between respiration, end-tidal CO2, and BOLD signals in resting-state fMRI , 2009, NeuroImage.

[47]  Anjali Krishnan,et al.  Cluster-extent based thresholding in fMRI analyses: Pitfalls and recommendations , 2014, NeuroImage.

[48]  Andrew D. Engell,et al.  The Neural Bases of Cognitive Conflict and Control in Moral Judgment , 2004, Neuron.

[49]  M. Baker 1,500 scientists lift the lid on reproducibility , 2016, Nature.

[50]  E. Wagenmakers A practical solution to the pervasive problems ofp values , 2007, Psychonomic bulletin & review.

[51]  Elizabeth Gilbert,et al.  Reproducibility Project: Results (Part of symposium called "The Reproducibility Project: Estimating the Reproducibility of Psychological Science") , 2014 .

[52]  CM Bennett,et al.  Neural correlates of interspecies perspective taking in the post-mortem Atlantic Salmon: an argument for multiple comparisons correction , 2009, NeuroImage.

[53]  Jacob Cohen,et al.  The earth is round (p < .05): Rejoinder. , 1995 .

[54]  Gregory Francis,et al.  Too good to be true: Publication bias in two prominent studies from experimental psychology , 2012, Psychonomic Bulletin & Review.

[55]  Karsten Mueller,et al.  Commentary: Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates , 2017, Front. Hum. Neurosci..

[56]  Jeffrey N. Rouder,et al.  Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications , 2017, Psychonomic Bulletin & Review.

[57]  Daniel S. Margulies,et al.  NeuroVault.org: a web-based repository for collecting and sharing unthresholded statistical maps of the human brain , 2014, bioRxiv.

[58]  Karl J. Friston,et al.  Analysis of family‐wise error rates in statistical parametric mapping using random field theory , 2016, Human brain mapping.

[59]  Andrew Gelman,et al.  Why We (Usually) Don't Have to Worry About Multiple Comparisons , 2009, 0907.2478.

[60]  Karl J. Friston,et al.  Dynamic causal modelling , 2003, NeuroImage.